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BEGIN:VEVENT
SUMMARY:Tom Weston (Univ. Masschusetts Amherst)
DTSTART:20220120T230000Z
DTEND:20220121T000000Z
DTSTAMP:20260404T111445Z
UID:iwasawa_theory_virtual_seminar/2
DESCRIPTION:Title: Explicit Reciprocity Laws and Iwasawa Theory
for Modular Forms\nby Tom Weston (Univ. Masschusetts Amherst) as part
of Iwasawa theory Virtual Seminar\n\n\nAbstract\nA conjecture of Mazur an
d Tate predicts that analytic theta elements of\nmodular forms\, which enc
ode special values of L-functions\, should lie in\nthe Fitting ideal of th
eir Selmer groups over cyclotomic extensions. In\nthis talk we outline a
proof of this conjecture (up to scaling) for\np-power cyclotomic extension
s in the case that the modular form is\nnon-ordinary at p. The key tool i
s a general local construction of\ncohomology classes via the p-adic local
Langlands correspondence. This\nis joint work with Matthew Emerton and R
obert Pollack.\n
LOCATION:https://stable.researchseminars.org/talk/iwasawa_theory_virtual_s
eminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Katharina Muller (Universite Laval)
DTSTART:20220127T230000Z
DTEND:20220128T000000Z
DTSTAMP:20260404T111445Z
UID:iwasawa_theory_virtual_seminar/3
DESCRIPTION:Title: Class Groups and fine Selmer Groups\nby
Katharina Muller (Universite Laval) as part of Iwasawa theory Virtual Semi
nar\n\n\nAbstract\nStarting from a result by Lim-Murty relating classical
Iwasawa invariants of fine Selmer groups and $p$-class groups over the cyc
lotomic $\\mathbb{Z}_p$-extension\, we investigate generalizations of this
results for multiple $\\mathbb{Z}_p$-extensions and uniform p-adic Lie-ex
tensions. If time allows we will also discuss a density result for the wea
k Leopoldt conjecture. This is joined work with Sören Kleine.\n
LOCATION:https://stable.researchseminars.org/talk/iwasawa_theory_virtual_s
eminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Delbourgo (University of Waikato)
DTSTART:20220203T230000Z
DTEND:20220204T000000Z
DTSTAMP:20260404T111445Z
UID:iwasawa_theory_virtual_seminar/4
DESCRIPTION:Title: L-invariants attached to the symmetric squar
e representation\nby Daniel Delbourgo (University of Waikato) as part
of Iwasawa theory Virtual Seminar\n\n\nAbstract\nThe p-adic L-function att
ached to the symmetric square of a modular\nform vanishes at certain criti
cal twists\, even though the complex\nL-function does not. We'll survey wh
at is known about the first\nderivative of this p-adic L-function\, and th
en describe an algorithm\nto compute the first derivative for non-CM ellip
tic curves. This talk\nshould hopefully be accessible to graduate students
in number theory.\n
LOCATION:https://stable.researchseminars.org/talk/iwasawa_theory_virtual_s
eminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rylan Gajek-Leonard (Univ. Massachusetts Amherst)
DTSTART:20220210T230000Z
DTEND:20220211T000000Z
DTSTAMP:20260404T111445Z
UID:iwasawa_theory_virtual_seminar/5
DESCRIPTION:Title: Iwasawa Invariants of Modular Forms with $a_
p=0$\nby Rylan Gajek-Leonard (Univ. Massachusetts Amherst) as part of
Iwasawa theory Virtual Seminar\n\n\nAbstract\nMazur-Tate elements provide
a convenient method to study the\nanalytic Iwasawa theory of p-nonordinary
modular forms\, where the\nassociated p-adic L-functions have unbounded c
oefficients. The Iwasawa\ninvariants of Mazur-Tate elements are well-under
stood in the case of\nweight two modular forms\, where they can be related
to the growth of\np-Selmer groups and decompositions of the p-adic L-func
tion. At higher\nweights\, less is known. By constructing certain lifts to
the full Iwasawa\nalgebra\, we compute the Iwasawa invariants of Mazur-Ta
te elements for\nhigher weight modular forms with $a_p=0$ in terms of the
plus/minus\ninvariants of the p-adic L-function. Combined with results of\
nPollack-Weston\, this forces a relation between plus/minus (and Sprung's
\nsharp/flat) invariants at weights 2 and p+1.\n
LOCATION:https://stable.researchseminars.org/talk/iwasawa_theory_virtual_s
eminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Debanjana Kundu (University of British Columbia)
DTSTART:20220217T230000Z
DTEND:20220218T000000Z
DTSTAMP:20260404T111445Z
UID:iwasawa_theory_virtual_seminar/6
DESCRIPTION:Title: Fine Selmer Groups and Duality\nby Deban
jana Kundu (University of British Columbia) as part of Iwasawa theory Virt
ual Seminar\n\n\nAbstract\nIn Iwasawa Theory of $p$-adic Representations (
1989)\, R. Greenberg developed an Iwasawa theory for $p$-ordinary motives
. In particular\, he showed that the $p$-Selmer group over the cyclotomic
$\\mathbb{Z}_p$ extension satisfies an algebraic functional equation. In t
he intervening years\, this strategy has been extended by several authors
to prove functional equations in other settings. After discussing the hist
ory of these results\, I will report on joint work with J. Hatley\, A. Lei
\, and J.Ray where we take the first steps in trying to prove an algebraic
functional equation for the fine Selmer group.\n
LOCATION:https://stable.researchseminars.org/talk/iwasawa_theory_virtual_s
eminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonio Cauchi (Concordia University)
DTSTART:20220224T230000Z
DTEND:20220225T000000Z
DTSTAMP:20260404T111445Z
UID:iwasawa_theory_virtual_seminar/7
DESCRIPTION:Title: On refined conjectures of Birch and Swinnert
on-Dyer type in the Rankin-Selberg setting\nby Antonio Cauchi (Concord
ia University) as part of Iwasawa theory Virtual Seminar\n\n\nAbstract\nIn
the late 80's\, Mazur and Tate proposed conjectures on the structure\nof
the Fitting ideals of Selmer groups over number fields of elliptic curves\
nover Q. These conjectures are aimed to refine Birch and Swinnerton-Dyer t
ype\nconjectures over number fields as well as the Iwasawa main conjecture
s over the\ncyclotomic $\\mathbb{Z}_p$-tower of Q. Results in this direct
ion have been obtained by Kim\nand Kurihara\, who studied the Fitting idea
ls over finite sub-extensions of the\ncyclotomic $\\mathbb{Z}_p$-extension
of Q.\n\nIn this talk\, I will describe results analogous to theirs on th
e Fitting ideals\nover the finite layers of the cyclotomic $\\mathbb{Z}_p$
-extension of Q of Selmer groups\nattached to the Rankin-Selberg convoluti
on of two modular forms f and g. In the\ncase where f corresponds to an e
lliptic curve E/Q and g to a two-dimensional\nodd irreducible Artin repres
entation with splitting field F\, I will explain how\nour results give an
upper bound of the dimension of the g-isotypic component of\nthe Mordell-W
eil group of E over the finite layers of the cyclotomic\n$\\mathbb{Z}_p$-e
xtension of F. This is joint work with Antonio Lei.\n
LOCATION:https://stable.researchseminars.org/talk/iwasawa_theory_virtual_s
eminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesc Castella (UC Santa Barbara)
DTSTART:20220303T230000Z
DTEND:20220304T000000Z
DTSTAMP:20260404T111445Z
UID:iwasawa_theory_virtual_seminar/8
DESCRIPTION:Title: Selmer classes on CM elliptic curves of rank
2\nby Francesc Castella (UC Santa Barbara) as part of Iwasawa theory
Virtual Seminar\n\n\nAbstract\nLet E be an elliptic curve over Q\, and let
p be a prime of good ordinary reduction for E. Following the pioneering w
ork of Skinner (and independently Wei Zhang) from about 8 years ago\, ther
e is a growing number of results in the direction of a p-converse to a the
orem of Gross-Zagier and Kolyvagin\, showing that if the p-adic Selmer gro
up of E is 1-dimensional\, then a Heegner point on E has infinite order. I
n this talk\, I'll report on the proof of an analogue of Skinner's result
in the rank 2 case\, in which Heegner points are replaced by certain gener
alized Kato classes introduced by Darmon-Rotger. For E without CM\, such a
n analogue was obtained in an earlier work with M.-L. Hsieh\, and in this
talk I'll focus on the CM case\, whose proof uses a different set of ideas
.\n
LOCATION:https://stable.researchseminars.org/talk/iwasawa_theory_virtual_s
eminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isabella Negrini (McGill University)
DTSTART:20220310T230000Z
DTEND:20220311T000000Z
DTSTAMP:20260404T111445Z
UID:iwasawa_theory_virtual_seminar/9
DESCRIPTION:Title: A Shimura-Shintani correspondence for rigid
analytic cocycles\nby Isabella Negrini (McGill University) as part of
Iwasawa theory Virtual Seminar\n\n\nAbstract\nIn their paper Singular modu
li for real quadratic fields: a rigid\n analytic approach\, Darmon and Von
k introduced rigid meromorphic cocycles\,\n i.e. elements of $H^1(SL_2(\\m
athbb{Z}[1/p])\, M^x)$ where $M^x$ is the multiplicative\n group of rigid
meromorphic functions on the p-adic upper-half plane.\n Their values at RM
points belong to narrow ring class fields of real\n quadratic fields and
behave analogously to CM values of modular functions\n on $SL_2(\\mathbb{Z
})\\backslash H$. In this talk\, I will present some progress towards\n de
veloping a Shimura-Shintani correspondence in this setting.\n
LOCATION:https://stable.researchseminars.org/talk/iwasawa_theory_virtual_s
eminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonio Lei (Universite Laval)
DTSTART:20220317T220000Z
DTEND:20220317T230000Z
DTSTAMP:20260404T111445Z
UID:iwasawa_theory_virtual_seminar/10
DESCRIPTION:Title: Asymptotic formula for Tate--Shafarevich gr
oups of $p$-supersingular elliptic curves over anticyclotomic extensions\nby Antonio Lei (Universite Laval) as part of Iwasawa theory Virtual Se
minar\n\n\nAbstract\nLet $p\\ge 5$ be a prime number and $E/\\mathbf{Q}$ a
n elliptic curve with good supersingular reduction at $p$. Under the gener
alized Heegner hypothesis\, we investigate the $p$-primary subgroups of th
e Tate--Shafarevich groups of $E$ over number fields contained inside the
anticyclotomic $\\mathbf{Z}_p$-extension of an imaginary quadratic field w
here $p$ splits. This is joint work with Meng Fai Lim and Katharina Muelle
r.\n
LOCATION:https://stable.researchseminars.org/talk/iwasawa_theory_virtual_s
eminar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Naomi Sweeting (Harvard)
DTSTART:20220324T220000Z
DTEND:20220324T230000Z
DTSTAMP:20260404T111445Z
UID:iwasawa_theory_virtual_seminar/11
DESCRIPTION:Title: Kolyvagin's conjecture\, bipartite Euler sy
stems\, and higher congruences of modular forms\nby Naomi Sweeting (Ha
rvard) as part of Iwasawa theory Virtual Seminar\n\n\nAbstract\nFor an ell
iptic curve E\, Kolyvagin used Heegner points to construct special Galois
cohomology classes valued in the torsion points of E. Under the conjectur
e that not all of these classes vanish\, he showed that they encode the Se
lmer rank of E. I will explain a proof of new cases of this conjecture tha
t builds on prior work of Wei Zhang. The proof naturally leads to a genera
lization of Kolyvagin's work in a complimentary "definite" setting\, where
Heegner points are replaced by special values of a quaternionic modular f
orm. I'll also explain an "ultrapatching" formalism which simplifies the S
elmer group arguments required for the proof.\n
LOCATION:https://stable.researchseminars.org/talk/iwasawa_theory_virtual_s
eminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lawrence Washington (University of Maryland)
DTSTART:20220331T220000Z
DTEND:20220331T230000Z
DTSTAMP:20260404T111445Z
UID:iwasawa_theory_virtual_seminar/12
DESCRIPTION:Title: Musings on $\\mu$\nby Lawrence Washingt
on (University of Maryland) as part of Iwasawa theory Virtual Seminar\n\n\
nAbstract\nIwasawa showed how to produce examples of $\\mathbb{Z}_p$-exten
sions where the mu-invariant (for class groups) is nonzero\, and this meth
od also yields extensions\nwhere the $\\ell$-part of the class group is un
bounded\, where $\\ell$ is a prime different from $p$. I'll review this co
nstruction and some related computations and then discuss\nsome ideas on w
hether this completely accounts for the behavior of the class number.\n
LOCATION:https://stable.researchseminars.org/talk/iwasawa_theory_virtual_s
eminar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chi-Yun Hsu (UCLA)
DTSTART:20220407T220000Z
DTEND:20220407T230000Z
DTSTAMP:20260404T111445Z
UID:iwasawa_theory_virtual_seminar/13
DESCRIPTION:Title: Partial classicality of Hilbert modular for
ms\nby Chi-Yun Hsu (UCLA) as part of Iwasawa theory Virtual Seminar\n\
n\nAbstract\nModular forms are global sections of certain line bundles on
the modular curve\, while p-adic overconvergent modular forms are defined
only over a strict neighborhood of the ordinary locus. The philosophy of c
lassicality theorems is that when the p-adic valuation of $U_p$-eigenvalue
is small compared to the weight (called a small slope condition)\, an ove
rconvergent $U_p$-eigenform is automatically classical\, namely\, it can b
e extended to the whole modular curve. In the case of Hilbert modular form
s\, there are the partially classical forms which are defined over a stric
t neighborhood of a “partially ordinary locus”. Modifying Kassaei’s
method of analytic continuation\, we show that under a weaker small slope
condition\, an overconvergent form is automatically partially classical.\n
LOCATION:https://stable.researchseminars.org/talk/iwasawa_theory_virtual_s
eminar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giovanni Rosso (Concordia University)
DTSTART:20220414T220000Z
DTEND:20220414T230000Z
DTSTAMP:20260404T111445Z
UID:iwasawa_theory_virtual_seminar/14
DESCRIPTION:Title: Overconvergent Eichler--Shimura morphism fo
r families of Siegel modular forms\nby Giovanni Rosso (Concordia Unive
rsity) as part of Iwasawa theory Virtual Seminar\n\n\nAbstract\nClassical
results of Eichler and Shimura decompose the cohomology of certain\nlocal
systems on the modular curve in terms of holomorphic and anti-holomorphic\
nmodular forms. A similar result has been proved by Faltings' for the etal
e\ncohomology of the modular curve and Falting's result has been partly\ng
eneralised to Coleman families by Andreatta-Iovita-Stevens.\nIn this talk\
, based on joint work with Hansheng Diao and Ju-Feng Wu\, I will\nexplain
how one constructs a morphism from the overconvergent cohomology of\n$GSp_
{2g}$ to the space of families of Siegel modular forms. This can be seen a
s a\nfirst step in an Eichler-Shimura decomposition for overconvergent coh
omology\nand involves a new definition of the sheaf of overconvergent Sieg
el modular\nforms using the Hodge--Tate map at infinite level. If time all
ows it\, I'll\nexplain how one can hope to use higher Coleman theory to fi
nd a complete\nanalogue of the classical Eichler--Shimura decomposition in
small slope.\n
LOCATION:https://stable.researchseminars.org/talk/iwasawa_theory_virtual_s
eminar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cedric Dion (Laval)
DTSTART:20220421T220000Z
DTEND:20220421T230000Z
DTSTAMP:20260404T111445Z
UID:iwasawa_theory_virtual_seminar/15
DESCRIPTION:Title: Arithmetic statistics for 2-bridge links\nby Cedric Dion (Laval) as part of Iwasawa theory Virtual Seminar\n\n\nA
bstract\nLet p be a fixed odd prime number. A famous theorem due to Iwasaw
a gives a formula for the rate of growth of the p-class group when the fie
lds vary in a $\\mathbb{Z}_p$-extension of a number field. In this talk\,
based on joint work with Anwesh Ray\, we study the topological analogue of
Iwasawa theory for knots or\, more generally\, for links which are disjoi
nt union of knots. In this setting\, one can show that the lambda-invarian
t associated to a $\\mathbb{Z}_p$-cover of a link with at least 2 componen
ts is always greater than 0. We give explicit formulae to detect when the
case $\\mu=0$ and $\\lambda=1$ do occur\, at least in the case of 2 and 3-
components links. We then study the proportion of 2-components links for w
hich $\\mu=0$ and $\\lambda=1$ when the links are parametrized in Schubert
normal form. Backed by numerical evidence\, we conjecture that $\\mu=0$ f
or 100% of such links.\n
LOCATION:https://stable.researchseminars.org/talk/iwasawa_theory_virtual_s
eminar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Vallieres (California State U\, Chico)
DTSTART:20220428T220000Z
DTEND:20220428T230000Z
DTSTAMP:20260404T111445Z
UID:iwasawa_theory_virtual_seminar/16
DESCRIPTION:Title: On some theorems in graph theory analogous
to past results in Iwasawa theory\nby Daniel Vallieres (California Sta
te U\, Chico) as part of Iwasawa theory Virtual Seminar\n\n\nAbstract\nIn
the 1950s\, Iwasawa proved his celebrated theorem on the growth of\nthe p-
part of the class number in Zp-extensions of number fields. The growth\no
f the q-part\, where q is another rational prime distinct from p\, was stu
died\nby Washington and Sinnott among others. In this talk\, we will expl
ain our work\nin obtaining analogous results in graph theory for the numbe
r of spanning trees\nin some infinite towers of graphs analogous to $\\mat
hbb{Z}_p$-extensions of number fields.\nPart of this work is joint with Ke
vin McGown and part of this work is joint\nwith Antonio Lei.\n
LOCATION:https://stable.researchseminars.org/talk/iwasawa_theory_virtual_s
eminar/16/
END:VEVENT
END:VCALENDAR